On some arithmetic properties of a sequence related to the quotient of Fibonacci numbers

Chatchawan Panraksa; Aram Tangboonduangjit

On some arithmetic properties of a sequence related to the quotient of Fibonacci numbers

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3 Citations (Scopus)

Abstract

We examine the sequence (T_n)_n>1 of numbers: 1, 11, 61, 451, 3001, 20801, 141961,⋯ given by T_n = F_5n/(5F_n), where F_n is the Fibonacci number. Curious divisibility properties are obtained including related conditions resembling a strong divisibility sequence. In particular, we prove that all prime divisors of the numbers in this sequence end in one. Another result asserts that each integral power of a number in the sequence is a divisor of some other number in the sequence. Specifically, we prove that for any positive integers n and k, the term.

Original language	English
Pages (from-to)	21-28
Number of pages	8
Journal	Fibonacci Quarterly
Volume	55
Issue number	1
Publication status	Published - Feb 2017

Cite this

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abstract = "We examine the sequence (Tn)n>1 of numbers: 1, 11, 61, 451, 3001, 20801, 141961,⋯ given by Tn = F5n/(5Fn), where Fn is the Fibonacci number. Curious divisibility properties are obtained including related conditions resembling a strong divisibility sequence. In particular, we prove that all prime divisors of the numbers in this sequence end in one. Another result asserts that each integral power of a number in the sequence is a divisor of some other number in the sequence. Specifically, we prove that for any positive integers n and k, the term.",

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N2 - We examine the sequence (Tn)n>1 of numbers: 1, 11, 61, 451, 3001, 20801, 141961,⋯ given by Tn = F5n/(5Fn), where Fn is the Fibonacci number. Curious divisibility properties are obtained including related conditions resembling a strong divisibility sequence. In particular, we prove that all prime divisors of the numbers in this sequence end in one. Another result asserts that each integral power of a number in the sequence is a divisor of some other number in the sequence. Specifically, we prove that for any positive integers n and k, the term.

AB - We examine the sequence (Tn)n>1 of numbers: 1, 11, 61, 451, 3001, 20801, 141961,⋯ given by Tn = F5n/(5Fn), where Fn is the Fibonacci number. Curious divisibility properties are obtained including related conditions resembling a strong divisibility sequence. In particular, we prove that all prime divisors of the numbers in this sequence end in one. Another result asserts that each integral power of a number in the sequence is a divisor of some other number in the sequence. Specifically, we prove that for any positive integers n and k, the term.

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On some arithmetic properties of a sequence related to the quotient of Fibonacci numbers

Abstract

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